I think Happo Giri means eight directional excersise or something close. Chuck will know.
In my dojo and most I have visted the Shomenuchi Ikkyo version seems to be the most popular. I have seen other types like Ikkyo Tenkan done, but I think the main point of these excersises is to teach teach how to be aware that an attack can come from any direction. The different flavors of Happo Giri Undo teach slightly different things, but I think it's just like knowing different ways to do a technique. It makes you more versatile.